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Translations and Mapping Notation
Translations and Mapping Notation

Occupation Games on Graphs in which the Second Player
Occupation Games on Graphs in which the Second Player

Vertex cover in cubic graphs with large girth
Vertex cover in cubic graphs with large girth

2. ALGORITHM ANALYSIS ‣ computational
2. ALGORITHM ANALYSIS ‣ computational

Notes for Lecture 11
Notes for Lecture 11

... 1. No polynomial time algorithm for A exists or 2. We are not smart. Open problem: PNP? ...
lecture1212
lecture1212

5.7A Vertex Form Parabola
5.7A Vertex Form Parabola

analysis of algorithms
analysis of algorithms

Convolutional neural network of Graphs without any a
Convolutional neural network of Graphs without any a

... Objectives: Numerous problems (drug property prediction, IP networks, social networks,. . . ) involve data which do not lie on an Eucidean space but which are efficiently represented through graph data structures (often with attributes on nodes and/or edges). The richness of this type of data combin ...
Q 9.1 Find a topological ordering for the graph in Figure 9.79
Q 9.1 Find a topological ordering for the graph in Figure 9.79

Graphs - Skinners` School Physics
Graphs - Skinners` School Physics

... using a ruler for a straight line graph, 4. or draw free-hand for a curved graph ...
How Science works : Graphs
How Science works : Graphs

... 3. Draw a line of best fit using a ruler for a straight line graph, 4. or draw free-hand for a curved graph ...
Lecture No. 10(A) : Method of Conditional Probabilities 1 - CSE-IITM
Lecture No. 10(A) : Method of Conditional Probabilities 1 - CSE-IITM

Explicit construction of linear sized tolerant networks
Explicit construction of linear sized tolerant networks

Given any resolution rule, a planar straight line upward drawing of
Given any resolution rule, a planar straight line upward drawing of

... and if t(xj) = 0, aj is in bottom Since clause ci contains atleast one literal y with t(y) = 1 and atleast one literal z with t(z) = 0 there’s atleast one unflagged link in each row. So we allign the chain such that the flaggs from the remaining link point towards the unflagged link leading to “no c ...
Graphing Skills 1 - Scott County Schools
Graphing Skills 1 - Scott County Schools

Abstract
Abstract

Lecture 16
Lecture 16

Lecture 17
Lecture 17

The Isoperimetric Number of Random Regular Graphs
The Isoperimetric Number of Random Regular Graphs

Slides
Slides

MaxFlow.pdf
MaxFlow.pdf

Document
Document

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Shortest Path

Where are the hard problems
Where are the hard problems

< 1 2 >

Clique problem



In computer science, the clique problem refers to any of the problems related to finding particular complete subgraphs (""cliques"") in a graph, i.e., sets of elements where each pair of elements is connected.For example, the maximum clique problem arises in the following real-world setting. Consider a social network, where the graph’s vertices represent people, and the graph’s edges represent mutual acquaintance. To find a largest subset of people who all know each other, one can systematically inspect all subsets, a process that is too time-consuming to be practical for social networks comprising more than a few dozen people. Although this brute-force search can be improved by more efficient algorithms, all of these algorithms take exponential time to solve the problem. Therefore, much of the theory about the clique problem is devoted to identifying special types of graph that admit more efficient algorithms, or to establishing the computational difficulty of the general problem in various models of computation. Along with its applications in social networks, the clique problem also has many applications in bioinformatics and computational chemistry.Clique problems include: finding a maximum clique (largest clique by vertices),finding a maximum weight clique in a weighted graph,listing all maximal cliques (cliques that cannot be enlarged)solving the decision problem of testing whether a graph contains a clique larger than a given size.These problems are all hard: the clique decision problem is NP-complete (one of Karp's 21 NP-complete problems), the problem of finding the maximum clique is both fixed-parameter intractable and hard to approximate, and listing all maximal cliques may require exponential time as there exist graphs with exponentially many maximal cliques. Nevertheless, there are algorithms for these problems that run in exponential time or that handle certain more specialized input graphs in polynomial time.
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